Characterizations of space curves with 1-type Darboux instantaneous rotation vector

Kadri Arslan; H\; Mehmet \

doi:10.4134/CKMS.2016.31.2.379

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2016; 31(2): 379-388

Printed April 30, 2016

https://doi.org/10.4134/CKMS.2016.31.2.379

Characterizations of space curves with 1-type Darboux instantaneous rotation vector

Kadri Arslan, H\"{u}seyin Kocayi\v{g}it, and Mehmet \"{O}nder

Uluda University, Manisa Celal Bayar University, Manisa Celal Bayar University

Abstract

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Abstract

In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space $E^{3} $. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector.

Keywords: Darboux vector, Laplacian operator, helix

MSC numbers: Primary 14H45, 14H50, 53A04